PB(OH)2 + HNO3 = PB(NO3)2 + H2O - Chemical Equation Balancer

To balance the equation PB(OH)2 + HNO3 = PB(NO3)2 + H2O using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.

Step 1: Label Each Compound With a Variable

Label each compound (reactant or product) in the equation with a variable đồ sộ represent the unknown coefficients.

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a PB(OH)₂ + b HNO₃ = c PB(NO₃)₂ + d H₂O

Step 2: Create a System of Equations

Create an equation for each element (P, B, O, H, N) where each term represents the number of atoms of the element in each reactant or product.

P:	1a	+	0b	=	1c	+	0d
B:	1a	+	0b	=	1c	+	0d
O:	2a	+	3b	=	6c	+	1d
H:	2a	+	1b	=	0c	+	2d
N:	0a	+	1b	=	2c	+	0d

Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.

1a - 1c = 0
1a - 1c = 0
2a + 3b - 6c - 1d = 0
2a + 1b - 2d = 0
1b - 2c = 0

Use your graphing calculator's rref() function (or an online rref calculator) đồ sộ convert the following matrix into reduced row-echelon-form:

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[ 1	 0	-1	 0	0]
[ 1	 0	-1	 0	0]
[ 2	 3	-6	-1	0]
[ 2	 1	 0	-2	0]
[ 0	 1	-2	 0	0]

The resulting matrix can be used đồ sộ determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result đồ sộ get the lowest, whole integer values.

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a = 1 (PB(OH)2)
b = 2 (HNO3)
c = 1 (PB(NO3)2)
d = 2 (H2O)

Step 4: Substitute Coefficients and Verify Result

Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.

PB(OH)₂ + 2 HNO₃ = PB(NO₃)₂ + 2 H₂O